MinT - Best Known (135−44, 135, s)-Nets in Base 4

Best Known (135−44, 135, s)-Nets in Base 4

(135−44, 135, 240)-Net over F₄ — Constructive and digital

Digital (91, 135, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 45, 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]

(135−44, 135, 431)-Net over F₄ — Digital

Digital (91, 135, 431)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−44, 135, 14916)-Net in Base 4 — Upper bound on s

There is no (91, 135, 14917)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1898 034595 147431 630423 428475 844675 693239 083478 801602 148900 174213 828933 878956 497760 > 4¹³⁵ [i]