MinT - Best Known (32, 32+37, s)-Nets in Base 81

Best Known (32, 32+37, s)-Nets in Base 81

(32, 32+37, 370)-Net over F₈₁ — Constructive and digital

Digital (32, 69, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 69, 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]

(32, 32+37, 830)-Net over F₈₁ — Digital

Digital (32, 69, 830)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 32+37, 1530628)-Net in Base 81 — Upper bound on s

There is no (32, 69, 1530629)-net in base 81, because

1 times m-reduction [i] would yield (32, 68, 1530629)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 5983 870409 503460 127235 957142 494388 509010 365256 260337 712157 481423 348323 483015 663003 776471 001187 484785 361064 542073 398779 638500 137761 > 81⁶⁸ [i]