MinT - Best Known (70, 70+124, s)-Nets in Base 4

Best Known (70, 70+124, s)-Nets in Base 4

(70, 70+124, 66)-Net over F₄ — Constructive and digital

Digital (70, 194, 66)-net over F₄, using

t-expansion [i] based on digital (49, 194, 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]

(70, 70+124, 105)-Net over F₄ — Digital

Digital (70, 194, 105)-net over F₄, using

net from sequence [i] based on digital (70, 104)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
  - Drinfeld modules of rank 1 [i]

(70, 70+124, 560)-Net in Base 4 — Upper bound on s

There is no (70, 194, 561)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 631 591336 353729 241415 823431 182384 903772 862788 786239 576517 377287 260376 515532 069783 077316 478686 182632 703069 501439 856384 > 4¹⁹⁴ [i]