MinT - Best Known (146−46, 146, s)-Nets in Base 4

Best Known (146−46, 146, s)-Nets in Base 4

(146−46, 146, 240)-Net over F₄ — Constructive and digital

Digital (100, 146, 240)-net over F₄, using

t-expansion [i] based on digital (99, 146, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (99, 147, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 49, 80)-net over F₆₄, using
    - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]

(146−46, 146, 524)-Net over F₄ — Digital

Digital (100, 146, 524)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−46, 146, 20831)-Net in Base 4 — Upper bound on s

There is no (100, 146, 20832)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7962 511760 925896 518737 431787 617712 008503 897305 278327 909626 560928 543438 246146 143447 639647 > 4¹⁴⁶ [i]