MinT - Best Known (33, 88, s)-Nets in Base 64

Best Known (33, 88, s)-Nets in Base 64

(33, 88, 513)-Net over F₆₄ — Constructive and digital

Digital (33, 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]

(33, 88, 114532)-Net in Base 64 — Upper bound on s

There is no (33, 88, 114533)-net in base 64, because

1 times m-reduction [i] would yield (33, 87, 114533)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 731372 258500 810571 359438 134091 170152 611264 022869 025485 083776 820666 016963 175877 610697 329044 199859 069833 079981 667359 944537 986041 072713 946596 263794 985160 244016 > 64⁸⁷ [i]