MinT - Best Known (53−28, 53, s)-Nets in Base 4

Best Known (53−28, 53, s)-Nets in Base 4

(53−28, 53, 36)-Net over F₄ — Constructive and digital

Digital (25, 53, 36)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (4, 18, 15)-net over F₄, using
  - net from sequence [i] based on digital (4, 14)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]
2. digital (7, 35, 21)-net over F₄, using
  - net from sequence [i] based on digital (7, 20)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]

(53−28, 53, 51)-Net over F₄ — Digital

Digital (25, 53, 51)-net over F₄, using

net from sequence [i] based on digital (25, 50)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 25 and N(F) ≥ 51, using
  - Drinfeld modules of rank 1 [i]

(53−28, 53, 372)-Net in Base 4 — Upper bound on s

There is no (25, 53, 373)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 83 289648 183048 101177 227710 805336 > 4⁵³ [i]