MinT - Best Known (203−48, 203, s)-Nets in Base 4

Best Known (203−48, 203, s)-Nets in Base 4

(203−48, 203, 1036)-Net over F₄ — Constructive and digital

Digital (155, 203, 1036)-net over F₄, using

1 times m-reduction [i] based on digital (155, 204, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 51, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(203−48, 203, 2463)-Net over F₄ — Digital

Digital (155, 203, 2463)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−48, 203, 404244)-Net in Base 4 — Upper bound on s

There is no (155, 203, 404245)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 165 264272 748479 237777 739519 068143 210133 955689 290298 777800 326907 556905 709177 280048 395108 754030 860451 296583 828170 132606 759584 > 4²⁰³ [i]