MinT - Best Known (180−72, 180, s)-Nets in Base 4

Best Known (180−72, 180, s)-Nets in Base 4

(180−72, 180, 130)-Net over F₄ — Constructive and digital

Digital (108, 180, 130)-net over F₄, using

t-expansion [i] based on digital (105, 180, 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]

(180−72, 180, 267)-Net over F₄ — Digital

Digital (108, 180, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−72, 180, 4844)-Net in Base 4 — Upper bound on s

There is no (108, 180, 4845)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 350139 658412 825256 807124 125632 490990 548144 437624 165592 623844 479939 363804 491141 438056 127823 872326 870851 530545 > 4¹⁸⁰ [i]