MinT - Best Known (31, 31+49, s)-Nets in Base 81

Best Known (31, 31+49, s)-Nets in Base 81

(31, 31+49, 370)-Net over F₈₁ — Constructive and digital

Digital (31, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(31, 31+49, 551)-Net over F₈₁ — Digital

Digital (31, 80, 551)-net over F₈₁, using

t-expansion [i] based on digital (30, 80, 551)-net over F₈₁, using
- net from sequence [i] based on digital (30, 550)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 30 and N(F) ≥ 551, using
    - a curve from the manYPoints database [i]

(31, 31+49, 234610)-Net in Base 81 — Upper bound on s

There is no (31, 80, 234611)-net in base 81, because

1 times m-reduction [i] would yield (31, 79, 234611)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5 893036 533465 296670 525723 104057 448789 367627 956419 334078 283778 746106 677709 562115 143928 116680 303683 907226 343940 369628 799282 430915 790428 332162 669571 323521 > 81⁷⁹ [i]