MinT - Best Known (64, 195, s)-Nets in Base 4

Best Known (64, 195, s)-Nets in Base 4

(64, 195, 66)-Net over F₄ — Constructive and digital

Digital (64, 195, 66)-net over F₄, using

t-expansion [i] based on digital (49, 195, 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, 195, 99)-Net over F₄ — Digital

Digital (64, 195, 99)-net over F₄, using

t-expansion [i] based on digital (61, 195, 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, 195, 471)-Net in Base 4 — Upper bound on s

There is no (64, 195, 472)-net in base 4, because

1 times m-reduction [i] would yield (64, 194, 472)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 684 622227 004294 329624 298282 769677 898867 724127 302315 636400 562320 531541 151492 903939 409600 627731 894950 191552 900639 118695 > 4¹⁹⁴ [i]