MinT - Best Known (25, 25+59, s)-Nets in Base 7

Best Known (25, 25+59, s)-Nets in Base 7

(25, 25+59, 31)-Net over F₇ — Constructive and digital

Digital (25, 84, 31)-net over F₇, using

net from sequence [i] based on digital (25, 30)-sequence over F₇, using
- Niederreiter sequence [i]

(25, 25+59, 72)-Net over F₇ — Digital

Digital (25, 84, 72)-net over F₇, using

t-expansion [i] based on digital (22, 84, 72)-net over F₇, using
- net from sequence [i] based on digital (22, 71)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 22 and N(F) ≥ 72, using
    - an algebraic function field over â„¤₇ by Yeo [i]

(25, 25+59, 491)-Net in Base 7 — Upper bound on s

There is no (25, 84, 492)-net in base 7, because

1 times m-reduction [i] would yield (25, 83, 492)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 14273 447054 811506 754462 743968 806230 070723 071122 548726 688493 393397 644713 > 7⁸³ [i]