MinT - Best Known (62, 62+125, s)-Nets in Base 4

Best Known (62, 62+125, s)-Nets in Base 4

(62, 62+125, 66)-Net over F₄ — Constructive and digital

Digital (62, 187, 66)-net over F₄, using

t-expansion [i] based on digital (49, 187, 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]

(62, 62+125, 99)-Net over F₄ — Digital

Digital (62, 187, 99)-net over F₄, using

t-expansion [i] based on digital (61, 187, 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]

(62, 62+125, 461)-Net in Base 4 — Upper bound on s

There is no (62, 187, 462)-net in base 4, because

1 times m-reduction [i] would yield (62, 186, 462)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10517 742334 664272 622449 948826 416085 350983 872904 836896 781622 592401 619165 694744 369875 306727 548083 003375 420976 216000 > 4¹⁸⁶ [i]