MinT - Best Known (87, 87+120, s)-Nets in Base 4

Best Known (87, 87+120, s)-Nets in Base 4

(87, 87+120, 104)-Net over F₄ — Constructive and digital

Digital (87, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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]

(87, 87+120, 129)-Net over F₄ — Digital

Digital (87, 207, 129)-net over F₄, using

t-expansion [i] based on digital (81, 207, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(87, 87+120, 874)-Net in Base 4 — Upper bound on s

There is no (87, 207, 875)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43024 070967 069348 586318 940438 626928 499066 540919 910092 970382 633096 466570 445829 326615 645517 446850 599742 445234 532764 914931 160656 > 4²⁰⁷ [i]