MinT - Best Known (160−95, 160, s)-Nets in Base 4

Best Known (160−95, 160, s)-Nets in Base 4

(160−95, 160, 66)-Net over F₄ — Constructive and digital

Digital (65, 160, 66)-net over F₄, using

t-expansion [i] based on digital (49, 160, 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]

(160−95, 160, 99)-Net over F₄ — Digital

Digital (65, 160, 99)-net over F₄, using

t-expansion [i] based on digital (61, 160, 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]

(160−95, 160, 628)-Net in Base 4 — Upper bound on s

There is no (65, 160, 629)-net in base 4, because

1 times m-reduction [i] would yield (65, 159, 629)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 550629 376777 493637 904560 421848 723652 606199 551914 858061 540436 499673 236363 665666 458215 120594 140560 > 4¹⁵⁹ [i]