MinT - Best Known (78−50, 78, s)-Nets in Base 7

Best Known (78−50, 78, s)-Nets in Base 7

(78−50, 78, 32)-Net over F₇ — Constructive and digital

Digital (28, 78, 32)-net over F₇, using

t-expansion [i] based on digital (27, 78, 32)-net over F₇, using
- net from sequence [i] based on digital (27, 31)-sequence over F₇, using
  - Niederreiter sequence [i]

(78−50, 78, 78)-Net over F₇ — Digital

Digital (28, 78, 78)-net over F₇, using

t-expansion [i] based on digital (27, 78, 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]

(78−50, 78, 718)-Net in Base 7 — Upper bound on s

There is no (28, 78, 719)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 833877 419719 676083 155387 451556 765224 625346 442325 555204 432501 125195 > 7⁷⁸ [i]