MinT - Best Known (23, 23+58, s)-Nets in Base 7

Best Known (23, 23+58, s)-Nets in Base 7

(23, 23+58, 30)-Net over F₇ — Constructive and digital

Digital (23, 81, 30)-net over F₇, using

net from sequence [i] based on digital (23, 29)-sequence over F₇, using
- Niederreiter sequence [i]

(23, 23+58, 72)-Net over F₇ — Digital

Digital (23, 81, 72)-net over F₇, using

t-expansion [i] based on digital (22, 81, 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]

(23, 23+58, 427)-Net in Base 7 — Upper bound on s

There is no (23, 81, 428)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 293 092186 307061 339991 980661 329625 281628 749548 678309 496001 154125 353001 > 7⁸¹ [i]