MinT - Best Known (36, 77, s)-Nets in Base 64

Best Known (36, 77, s)-Nets in Base 64

(36, 77, 513)-Net over F₆₄ — Constructive and digital

Digital (36, 77, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 77, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(36, 77, 771)-Net over F₆₄ — Digital

Digital (36, 77, 771)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 77, 962598)-Net in Base 64 — Upper bound on s

There is no (36, 77, 962599)-net in base 64, because

1 times m-reduction [i] would yield (36, 76, 962599)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 186072 880862 452779 385962 282626 330565 894997 968997 721558 868353 260360 451166 843368 589649 456041 612991 077851 280696 814366 804556 348336 885526 693346 > 64⁷⁶ [i]