MinT - Best Known (29, 29+59, s)-Nets in Base 64

Best Known (29, 29+59, s)-Nets in Base 64

(29, 29+59, 513)-Net over F₆₄ — Constructive and digital

Digital (29, 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]

(29, 29+59, 48550)-Net in Base 64 — Upper bound on s

There is no (29, 88, 48551)-net in base 64, because

1 times m-reduction [i] would yield (29, 87, 48551)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 735189 842151 405432 389751 721817 479687 798440 070538 255529 571703 662530 831751 702917 895368 084079 269439 096521 667668 398337 281091 833102 174729 627841 323822 120800 696680 > 64⁸⁷ [i]