MinT - Best Known (30, 69, s)-Nets in Base 64

Best Known (30, 69, s)-Nets in Base 64

(30, 69, 513)-Net over F₆₄ — Constructive and digital

Digital (30, 69, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 69, 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]

(30, 69, 366510)-Net in Base 64 — Upper bound on s

There is no (30, 69, 366511)-net in base 64, because

1 times m-reduction [i] would yield (30, 68, 366511)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 661 056358 632950 070859 254628 258976 936670 005441 735828 871052 456543 230096 802535 216954 571476 846061 975794 310982 031730 055238 008840 > 64⁶⁸ [i]