MinT - Best Known (80, 80+162, s)-Nets in Base 4

Best Known (80, 80+162, s)-Nets in Base 4

(80, 80+162, 104)-Net over F₄ — Constructive and digital

Digital (80, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(80, 80+162, 112)-Net over F₄ — Digital

Digital (80, 242, 112)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(80, 80+162, 584)-Net in Base 4 — Upper bound on s

There is no (80, 242, 585)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 400614 118965 025937 302360 834318 666889 323888 847354 218966 294927 867055 683025 948304 802909 875696 415186 262737 510319 467508 459879 559790 281803 185548 155264 > 4²⁴² [i]