MinT - Best Known (228−138, 228, s)-Nets in Base 4

Best Known (228−138, 228, s)-Nets in Base 4

(228−138, 228, 104)-Net over F₄ — Constructive and digital

Digital (90, 228, 104)-net over F₄, using

t-expansion [i] based on digital (73, 228, 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]

(228−138, 228, 129)-Net over F₄ — Digital

Digital (90, 228, 129)-net over F₄, using

t-expansion [i] based on digital (81, 228, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(228−138, 228, 807)-Net in Base 4 — Upper bound on s

There is no (90, 228, 808)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 196809 478334 897809 525127 549821 339195 859265 912312 276528 340438 248840 244122 117300 785929 511071 271939 097273 691596 363913 447907 518237 439797 548244 > 4²²⁸ [i]