MinT - Best Known (79−41, 79, s)-Nets in Base 64

Best Known (79−41, 79, s)-Nets in Base 64

(79−41, 79, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 79, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 79, 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]

(79−41, 79, 944)-Net over F₆₄ — Digital

Digital (38, 79, 944)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−41, 79, 1459031)-Net in Base 64 — Upper bound on s

There is no (38, 79, 1459032)-net in base 64, because

1 times m-reduction [i] would yield (38, 78, 1459032)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 762 151237 304477 197323 609675 250610 675979 752343 289658 041657 514109 080223 626772 375925 923520 249128 571590 871691 727136 919692 460611 485727 823147 404879 > 64⁷⁸ [i]