MinT - Best Known (63, 63+79, s)-Nets in Base 4

Best Known (63, 63+79, s)-Nets in Base 4

(63, 63+79, 66)-Net over F₄ — Constructive and digital

Digital (63, 142, 66)-net over F₄, using

t-expansion [i] based on digital (49, 142, 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]

(63, 63+79, 99)-Net over F₄ — Digital

Digital (63, 142, 99)-net over F₄, using

t-expansion [i] based on digital (61, 142, 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]

(63, 63+79, 739)-Net in Base 4 — Upper bound on s

There is no (63, 142, 740)-net in base 4, because

1 times m-reduction [i] would yield (63, 141, 740)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 022110 153911 046597 728368 447825 790360 839588 754405 017459 658769 372757 047064 450419 881648 > 4¹⁴¹ [i]