MinT - Best Known (36, 107, s)-Nets in Base 27

Best Known (36, 107, s)-Nets in Base 27

(36, 107, 114)-Net over F₂₇ — Constructive and digital

Digital (36, 107, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 107, 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]

(36, 107, 172)-Net in Base 27 — Constructive

(36, 107, 172)-net in base 27, using

t-expansion [i] based on (34, 107, 172)-net in base 27, using
- 1 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]

(36, 107, 244)-Net over F₂₇ — Digital

Digital (36, 107, 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]

(36, 107, 11550)-Net in Base 27 — Upper bound on s

There is no (36, 107, 11551)-net in base 27, because

1 times m-reduction [i] would yield (36, 106, 11551)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 53 166072 499685 542150 658615 231714 985537 776503 352180 126527 050342 256846 427877 546311 451573 900472 980313 991083 004335 851348 037124 182425 064272 472298 788318 941171 > 27¹⁰⁶ [i]