MinT - Best Known (76, 76+126, s)-Nets in Base 4

Best Known (76, 76+126, s)-Nets in Base 4

(76, 76+126, 104)-Net over F₄ — Constructive and digital

Digital (76, 202, 104)-net over F₄, using

t-expansion [i] based on digital (73, 202, 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]

(76, 76+126, 112)-Net over F₄ — Digital

Digital (76, 202, 112)-net over F₄, using

t-expansion [i] based on digital (73, 202, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(76, 76+126, 639)-Net in Base 4 — Upper bound on s

There is no (76, 202, 640)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 42 769893 288549 711374 251065 026739 330178 055311 144320 760861 954454 962074 325252 764348 858635 205066 743854 600318 595329 937283 097933 > 4²⁰² [i]