MinT - Best Known (151−76, 151, s)-Nets in Base 4

Best Known (151−76, 151, s)-Nets in Base 4

(151−76, 151, 104)-Net over F₄ — Constructive and digital

Digital (75, 151, 104)-net over F₄, using

t-expansion [i] based on digital (73, 151, 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]

(151−76, 151, 112)-Net over F₄ — Digital

Digital (75, 151, 112)-net over F₄, using

t-expansion [i] based on digital (73, 151, 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]

(151−76, 151, 1205)-Net in Base 4 — Upper bound on s

There is no (75, 151, 1206)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 325183 512667 963590 645256 118101 703443 365853 398780 981366 475547 135759 562007 693244 504680 718000 > 4¹⁵¹ [i]