MinT - Best Known (78−49, 78, s)-Nets in Base 64

Best Known (78−49, 78, s)-Nets in Base 64

(78−49, 78, 513)-Net over F₆₄ — Constructive and digital

Digital (29, 78, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 78, 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]

(78−49, 78, 97005)-Net in Base 64 — Upper bound on s

There is no (29, 78, 97006)-net in base 64, because

1 times m-reduction [i] would yield (29, 77, 97006)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11 909960 356418 451700 764939 216215 028869 887859 031481 987245 227866 908087 047616 903263 266799 855950 151660 806680 317827 561283 634695 840125 640014 279594 > 64⁷⁷ [i]