MinT - Best Known (222−129, 222, s)-Nets in Base 4

Best Known (222−129, 222, s)-Nets in Base 4

(222−129, 222, 104)-Net over F₄ — Constructive and digital

Digital (93, 222, 104)-net over F₄, using

t-expansion [i] based on digital (73, 222, 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]

(222−129, 222, 144)-Net over F₄ — Digital

Digital (93, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 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]

(222−129, 222, 934)-Net in Base 4 — Upper bound on s

There is no (93, 222, 935)-net in base 4, because

1 times m-reduction [i] would yield (93, 221, 935)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 548282 552408 362356 174559 962453 200722 413981 078701 137161 953065 147332 475983 386018 367197 202968 528368 614744 212433 630911 241700 913311 557230 > 4²²¹ [i]