MinT - Best Known (207−128, 207, s)-Nets in Base 4

Best Known (207−128, 207, s)-Nets in Base 4

(207−128, 207, 104)-Net over F₄ — Constructive and digital

Digital (79, 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]

(207−128, 207, 112)-Net over F₄ — Digital

Digital (79, 207, 112)-net over F₄, using

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

(207−128, 207, 677)-Net in Base 4 — Upper bound on s

There is no (79, 207, 678)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46037 961143 512218 251639 220039 747116 287705 706855 042068 457554 896576 080871 982144 807776 433988 852210 389797 790338 819567 011780 437978 > 4²⁰⁷ [i]