MinT - Best Known (174−41, 174, s)-Nets in Base 4

Best Known (174−41, 174, s)-Nets in Base 4

(174−41, 174, 1036)-Net over F₄ — Constructive and digital

Digital (133, 174, 1036)-net over F₄, using

4² times duplication [i] based on digital (131, 172, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 43, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(174−41, 174, 2206)-Net over F₄ — Digital

Digital (133, 174, 2206)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−41, 174, 446671)-Net in Base 4 — Upper bound on s

There is no (133, 174, 446672)-net in base 4, because

1 times m-reduction [i] would yield (133, 173, 446672)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 347269 686514 434234 102210 935782 388210 758595 332398 807553 293353 343069 055660 394618 030038 059109 787416 475036 > 4¹⁷³ [i]