MinT - Best Known (66, 66+128, s)-Nets in Base 4

Best Known (66, 66+128, s)-Nets in Base 4

(66, 66+128, 66)-Net over F₄ — Constructive and digital

Digital (66, 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]

(66, 66+128, 99)-Net over F₄ — Digital

Digital (66, 194, 99)-net over F₄, using

t-expansion [i] based on digital (61, 194, 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]

(66, 66+128, 498)-Net in Base 4 — Upper bound on s

There is no (66, 194, 499)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 653 012232 492432 911109 199041 602474 543481 832881 262014 115446 229658 832781 881822 887014 067290 991978 290326 812968 771039 264849 > 4¹⁹⁴ [i]