MinT - Best Known (204−48, 204, s)-Nets in Base 4

Best Known (204−48, 204, s)-Nets in Base 4

(204−48, 204, 1040)-Net over F₄ — Constructive and digital

Digital (156, 204, 1040)-net over F₄, using

trace code for nets [i] based on digital (3, 51, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(204−48, 204, 2536)-Net over F₄ — Digital

Digital (156, 204, 2536)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−48, 204, 428283)-Net in Base 4 — Upper bound on s

There is no (156, 204, 428284)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 661 063830 230828 155385 895242 762650 432738 735758 342016 533085 448583 146934 619805 955329 853646 657875 161541 222371 170880 408682 074731 > 4²⁰⁴ [i]