MinT - Best Known (104, 104+156, s)-Nets in Base 4

Best Known (104, 104+156, s)-Nets in Base 4

(104, 104+156, 104)-Net over F₄ — Constructive and digital

Digital (104, 260, 104)-net over F₄, using

t-expansion [i] based on digital (73, 260, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(104, 104+156, 144)-Net over F₄ — Digital

Digital (104, 260, 144)-net over F₄, using

t-expansion [i] based on digital (91, 260, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(104, 104+156, 948)-Net in Base 4 — Upper bound on s

There is no (104, 260, 949)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 672335 131171 787530 802197 561386 643386 031819 807574 530708 627358 265803 574272 532425 749976 639928 310364 000732 025550 207869 794593 445835 245105 360359 712350 656735 348880 > 4²⁶⁰ [i]