MinT - Best Known (81−63, 81, s)-Nets in Base 7

Best Known (81−63, 81, s)-Nets in Base 7

(81−63, 81, 26)-Net over F₇ — Constructive and digital

Digital (18, 81, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(81−63, 81, 51)-Net over F₇ — Digital

Digital (18, 81, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(81−63, 81, 294)-Net in Base 7 — Upper bound on s

There is no (18, 81, 295)-net in base 7, because

1 times m-reduction [i] would yield (18, 80, 295)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 44 175438 181876 635449 529356 525096 690147 447354 645118 820142 646450 778375 > 7⁸⁰ [i]