MinT - Best Known (104, 104+153, s)-Nets in Base 4

Best Known (104, 104+153, s)-Nets in Base 4

(104, 104+153, 104)-Net over F₄ — Constructive and digital

Digital (104, 257, 104)-net over F₄, using

t-expansion [i] based on digital (73, 257, 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+153, 144)-Net over F₄ — Digital

Digital (104, 257, 144)-net over F₄, using

t-expansion [i] based on digital (91, 257, 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+153, 973)-Net in Base 4 — Upper bound on s

There is no (104, 257, 974)-net in base 4, because

1 times m-reduction [i] would yield (104, 256, 974)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13638 274398 913260 030785 664133 569996 242268 118160 490567 943006 492712 206436 247301 853240 098086 376632 701898 148273 192949 791595 043155 045454 201918 826612 430457 655351 > 4²⁵⁶ [i]