MinT - Best Known (27, 27+66, s)-Nets in Base 7

Best Known (27, 27+66, s)-Nets in Base 7

(27, 27+66, 32)-Net over F₇ — Constructive and digital

Digital (27, 93, 32)-net over F₇, using

net from sequence [i] based on digital (27, 31)-sequence over F₇, using
- Niederreiter sequence [i]

(27, 27+66, 78)-Net over F₇ — Digital

Digital (27, 93, 78)-net over F₇, using

net from sequence [i] based on digital (27, 77)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 27 and N(F) ≥ 78, using
  - an algebraic function field by Teo [i]

(27, 27+66, 507)-Net in Base 7 — Upper bound on s

There is no (27, 93, 508)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 4 172949 626506 671974 736961 646910 918842 452343 951549 780557 998574 776915 775888 068073 > 7⁹³ [i]