MinT - Best Known (80, 80+158, s)-Nets in Base 4

Best Known (80, 80+158, s)-Nets in Base 4

(80, 80+158, 104)-Net over F₄ — Constructive and digital

Digital (80, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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+158, 112)-Net over F₄ — Digital

Digital (80, 238, 112)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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+158, 593)-Net in Base 4 — Upper bound on s

There is no (80, 238, 594)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212527 910509 594041 127718 019750 436281 265234 160911 034160 766730 338169 110876 911161 787884 662623 087294 174232 946820 472785 783010 574250 665300 260691 745688 > 4²³⁸ [i]