MinT - Best Known (102, 102+132, s)-Nets in Base 4

Best Known (102, 102+132, s)-Nets in Base 4

(102, 102+132, 104)-Net over F₄ — Constructive and digital

Digital (102, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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]

(102, 102+132, 144)-Net over F₄ — Digital

Digital (102, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 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]

(102, 102+132, 1101)-Net in Base 4 — Upper bound on s

There is no (102, 234, 1102)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 790 666143 706619 914274 571947 761398 121300 646732 624079 250380 953064 159870 305183 300443 450335 060086 543772 043898 948849 863405 829344 803892 552181 282518 > 4²³⁴ [i]