MinT - Best Known (170−94, 170, s)-Nets in Base 4

Best Known (170−94, 170, s)-Nets in Base 4

(170−94, 170, 104)-Net over F₄ — Constructive and digital

Digital (76, 170, 104)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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]

(170−94, 170, 112)-Net over F₄ — Digital

Digital (76, 170, 112)-net over F₄, using

t-expansion [i] based on digital (73, 170, 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]

(170−94, 170, 883)-Net in Base 4 — Upper bound on s

There is no (76, 170, 884)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 268298 100769 549736 485352 110651 483347 870217 810028 006754 488767 401565 583334 116133 848921 790415 844553 810620 > 4¹⁷⁰ [i]