MinT - Best Known (101−65, 101, s)-Nets in Base 27

Best Known (101−65, 101, s)-Nets in Base 27

(101−65, 101, 114)-Net over F₂₇ — Constructive and digital

Digital (36, 101, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 101, 114)-net over F₂₇, using
- net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
    - an explicitly constructive algebraic function field [i]

(101−65, 101, 172)-Net in Base 27 — Constructive

(36, 101, 172)-net in base 27, using

t-expansion [i] based on (34, 101, 172)-net in base 27, using
- 7 times m-reduction [i] based on (34, 108, 172)-net in base 27, using
  - base change [i] based on digital (7, 81, 172)-net over F₈₁, using
    - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
        a function field by SÃ©mirat [i]

(101−65, 101, 244)-Net over F₂₇ — Digital

Digital (36, 101, 244)-net over F₂₇, using

net from sequence [i] based on digital (36, 243)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 36 and N(F) ≥ 244, using
  - Drinfeld modules of rank 1 [i]

(101−65, 101, 14602)-Net in Base 27 — Upper bound on s

There is no (36, 101, 14603)-net in base 27, because

1 times m-reduction [i] would yield (36, 100, 14603)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137098 065401 385419 416626 558600 733106 454001 155473 368804 156855 659669 304445 027386 840201 804084 686242 723409 038751 501728 329937 087111 022859 169953 292481 > 27¹⁰⁰ [i]