MinT - Best Known (109, 109+148, s)-Nets in Base 4

Best Known (109, 109+148, s)-Nets in Base 4

(109, 109+148, 130)-Net over F₄ — Constructive and digital

Digital (109, 257, 130)-net over F₄, using

t-expansion [i] based on digital (105, 257, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(109, 109+148, 165)-Net over F₄ — Digital

Digital (109, 257, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(109, 109+148, 1106)-Net in Base 4 — Upper bound on s

There is no (109, 257, 1107)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 56234 999469 586890 455645 833537 259926 997270 490474 054584 597470 559683 075297 006680 753761 886067 604827 815402 731245 765213 524010 387371 918583 841150 227199 242522 104406 > 4²⁵⁷ [i]