MinT - Best Known (154−83, 154, s)-Nets in Base 4

Best Known (154−83, 154, s)-Nets in Base 4

(154−83, 154, 66)-Net over F₄ — Constructive and digital

Digital (71, 154, 66)-net over F₄, using

t-expansion [i] based on digital (49, 154, 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]

(154−83, 154, 105)-Net over F₄ — Digital

Digital (71, 154, 105)-net over F₄, using

t-expansion [i] based on digital (70, 154, 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]

(154−83, 154, 916)-Net in Base 4 — Upper bound on s

There is no (71, 154, 917)-net in base 4, because

1 times m-reduction [i] would yield (71, 153, 917)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 134 367563 753390 656698 459273 871468 804723 717358 868182 143702 489097 049575 173803 128949 161295 181888 > 4¹⁵³ [i]