MinT - Best Known (73−48, 73, s)-Nets in Base 7

Best Known (73−48, 73, s)-Nets in Base 7

(73−48, 73, 31)-Net over F₇ — Constructive and digital

Digital (25, 73, 31)-net over F₇, using

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

(73−48, 73, 72)-Net over F₇ — Digital

Digital (25, 73, 72)-net over F₇, using

t-expansion [i] based on digital (22, 73, 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]

(73−48, 73, 592)-Net in Base 7 — Upper bound on s

There is no (25, 73, 593)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 50 468020 971495 409389 156949 814424 929660 913128 358722 146784 112193 > 7⁷³ [i]