MinT - Best Known (35, 35+53, s)-Nets in Base 64

Best Known (35, 35+53, s)-Nets in Base 64

(35, 35+53, 513)-Net over F₆₄ — Constructive and digital

Digital (35, 88, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 88, 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]

(35, 35+53, 185215)-Net in Base 64 — Upper bound on s

There is no (35, 88, 185216)-net in base 64, because

1 times m-reduction [i] would yield (35, 87, 185216)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 729776 277263 548974 281481 654506 784511 062052 999116 078534 554393 647648 235015 413404 933930 867392 541750 994899 810400 965366 231572 114947 304960 108074 134121 292817 365097 > 64⁸⁷ [i]