MinT - Best Known (260−148, 260, s)-Nets in Base 4

Best Known (260−148, 260, s)-Nets in Base 4

(260−148, 260, 130)-Net over F₄ — Constructive and digital

Digital (112, 260, 130)-net over F₄, using

t-expansion [i] based on digital (105, 260, 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]

(260−148, 260, 165)-Net over F₄ — Digital

Digital (112, 260, 165)-net over F₄, using

t-expansion [i] based on digital (109, 260, 165)-net over F₄, using
- net from sequence [i] based on digital (109, 164)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
    - Drinfeld modules of rank 1 [i]

(260−148, 260, 1173)-Net in Base 4 — Upper bound on s

There is no (112, 260, 1174)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 513687 391293 636207 422879 159551 424836 496554 554781 225704 909162 374451 108342 358755 748169 270866 401280 569394 936385 439995 930247 642184 605985 264608 370972 459589 313640 > 4²⁶⁰ [i]