MinT - Best Known (160−84, 160, s)-Nets in Base 4

Best Known (160−84, 160, s)-Nets in Base 4

(160−84, 160, 104)-Net over F₄ — Constructive and digital

Digital (76, 160, 104)-net over F₄, using

t-expansion [i] based on digital (73, 160, 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]

(160−84, 160, 112)-Net over F₄ — Digital

Digital (76, 160, 112)-net over F₄, using

t-expansion [i] based on digital (73, 160, 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]

(160−84, 160, 1047)-Net in Base 4 — Upper bound on s

There is no (76, 160, 1048)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 139937 848398 903502 627191 300461 188310 851589 257913 036602 374548 207762 659638 054893 176204 610237 898176 > 4¹⁶⁰ [i]