MinT - Best Known (137−84, 137, s)-Nets in Base 4

Best Known (137−84, 137, s)-Nets in Base 4

(137−84, 137, 66)-Net over F₄ — Constructive and digital

Digital (53, 137, 66)-net over F₄, using

t-expansion [i] based on digital (49, 137, 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]

(137−84, 137, 91)-Net over F₄ — Digital

Digital (53, 137, 91)-net over F₄, using

t-expansion [i] based on digital (50, 137, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(137−84, 137, 472)-Net in Base 4 — Upper bound on s

There is no (53, 137, 473)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30793 702007 530810 211720 548521 989875 659175 706920 902143 819370 337072 931939 461766 998384 > 4¹³⁷ [i]