MinT - Best Known (147−83, 147, s)-Nets in Base 4

Best Known (147−83, 147, s)-Nets in Base 4

(147−83, 147, 66)-Net over F₄ — Constructive and digital

Digital (64, 147, 66)-net over F₄, using

t-expansion [i] based on digital (49, 147, 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]

(147−83, 147, 99)-Net over F₄ — Digital

Digital (64, 147, 99)-net over F₄, using

t-expansion [i] based on digital (61, 147, 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]

(147−83, 147, 716)-Net in Base 4 — Upper bound on s

There is no (64, 147, 717)-net in base 4, because

1 times m-reduction [i] would yield (64, 146, 717)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8268 958141 632266 652334 802714 361275 506588 469333 013586 095523 748651 406092 160487 383451 988512 > 4¹⁴⁶ [i]