MinT - Best Known (156−72, 156, s)-Nets in Base 4

Best Known (156−72, 156, s)-Nets in Base 4

(156−72, 156, 130)-Net over F₄ — Constructive and digital

Digital (84, 156, 130)-net over F₄, using

trace code for nets [i] based on digital (6, 78, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(156−72, 156, 149)-Net over F₄ — Digital

Digital (84, 156, 149)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−72, 156, 1905)-Net in Base 4 — Upper bound on s

There is no (84, 156, 1906)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8491 836601 167033 275030 779220 824036 169448 946314 378765 381412 319291 599640 227438 963545 904187 741020 > 4¹⁵⁶ [i]