MinT - Best Known (170−97, 170, s)-Nets in Base 4

Best Known (170−97, 170, s)-Nets in Base 4

(170−97, 170, 104)-Net over F₄ — Constructive and digital

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]

(170−97, 170, 112)-Net over F₄ — Digital

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]

(170−97, 170, 784)-Net in Base 4 — Upper bound on s

There is no (73, 170, 785)-net in base 4, because

1 times m-reduction [i] would yield (73, 169, 785)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 585032 797055 357632 044525 459208 876467 920737 558257 549217 662391 790750 157112 147585 856619 569593 977370 854808 > 4¹⁶⁹ [i]