MinT - Best Known (153−48, 153, s)-Nets in Base 4

Best Known (153−48, 153, s)-Nets in Base 4

(153−48, 153, 312)-Net over F₄ — Constructive and digital

Digital (105, 153, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 51, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(153−48, 153, 554)-Net over F₄ — Digital

Digital (105, 153, 554)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−48, 153, 22490)-Net in Base 4 — Upper bound on s

There is no (105, 153, 22491)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 130 450223 264869 419705 148442 329157 159735 721930 346595 304445 068179 388094 555464 141311 010790 127329 > 4¹⁵³ [i]