MinT - Best Known (28, 28+71, s)-Nets in Base 7

Best Known (28, 28+71, s)-Nets in Base 7

(28, 28+71, 32)-Net over F₇ — Constructive and digital

Digital (28, 99, 32)-net over F₇, using

t-expansion [i] based on digital (27, 99, 32)-net over F₇, using
- net from sequence [i] based on digital (27, 31)-sequence over F₇, using
  - Niederreiter sequence [i]

(28, 28+71, 78)-Net over F₇ — Digital

Digital (28, 99, 78)-net over F₇, using

t-expansion [i] based on digital (27, 99, 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]

(28, 28+71, 516)-Net in Base 7 — Upper bound on s

There is no (28, 99, 517)-net in base 7, because

1 times m-reduction [i] would yield (28, 98, 517)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 69439 522059 584417 367737 601563 602331 382231 547359 837424 961864 684157 658479 199401 942583 > 7⁹⁸ [i]