MinT - Best Known (100−70, 100, s)-Nets in Base 27

Best Known (100−70, 100, s)-Nets in Base 27

(100−70, 100, 114)-Net over F₂₇ — Constructive and digital

Digital (30, 100, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 100, 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]

(100−70, 100, 160)-Net in Base 27 — Constructive

(30, 100, 160)-net in base 27, using

base change [i] based on digital (5, 75, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(100−70, 100, 208)-Net over F₂₇ — Digital

Digital (30, 100, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 100, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(100−70, 100, 6556)-Net in Base 27 — Upper bound on s

There is no (30, 100, 6557)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 137075 547771 660800 104561 332060 344653 432718 042138 050741 459533 032573 335496 695148 772702 053517 784170 930519 172198 876045 421233 968709 899892 750056 554547 > 27¹⁰⁰ [i]