MinT - Best Known (208−97, 208, s)-Nets in Base 4

Best Known (208−97, 208, s)-Nets in Base 4

(208−97, 208, 130)-Net over F₄ — Constructive and digital

Digital (111, 208, 130)-net over F₄, using

t-expansion [i] based on digital (105, 208, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(208−97, 208, 185)-Net over F₄ — Digital

Digital (111, 208, 185)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−97, 208, 2427)-Net in Base 4 — Upper bound on s

There is no (111, 208, 2428)-net in base 4, because

1 times m-reduction [i] would yield (111, 207, 2428)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43075 207377 492041 068380 439404 604662 346507 615782 618453 162933 092306 546271 142838 658331 232135 791434 476078 075199 606210 543563 834425 > 4²⁰⁷ [i]