MinT - Best Known (64, 64+99, s)-Nets in Base 4

Best Known (64, 64+99, s)-Nets in Base 4

(64, 64+99, 66)-Net over F₄ — Constructive and digital

Digital (64, 163, 66)-net over F₄, using

t-expansion [i] based on digital (49, 163, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(64, 64+99, 99)-Net over F₄ — Digital

Digital (64, 163, 99)-net over F₄, using

t-expansion [i] based on digital (61, 163, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(64, 64+99, 583)-Net in Base 4 — Upper bound on s

There is no (64, 163, 584)-net in base 4, because

1 times m-reduction [i] would yield (64, 162, 584)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 34 458930 910247 486387 243851 447569 465899 607122 223978 529382 829863 348682 334495 461805 302949 254490 562668 > 4¹⁶² [i]