MinT - Best Known (193−132, 193, s)-Nets in Base 4

Best Known (193−132, 193, s)-Nets in Base 4

(193−132, 193, 66)-Net over F₄ — Constructive and digital

Digital (61, 193, 66)-net over F₄, using

t-expansion [i] based on digital (49, 193, 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]

(193−132, 193, 99)-Net over F₄ — Digital

Digital (61, 193, 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]

(193−132, 193, 435)-Net in Base 4 — Upper bound on s

There is no (61, 193, 436)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 161 332373 050558 644565 511993 246510 394407 544630 570135 061345 934874 629540 884548 001536 964655 581282 617827 054187 830245 271530 > 4¹⁹³ [i]